The second one is correct, in the case of first question both the question and the answer are wrong. Why you use "te", the subject is implicit in "buscas" (you - tu, second person, present tense). It is more simple, probably you make a mispelling mistake, use "de". For the answer you do not buy your self (cuando voy me compro), again is more simple:

1. ¿Qué buscas cuando vas de compras? is the question as Ricardfo says. the answer then is: Busco variedad de cosas cuando me voy de compras. OR rather than irse, since the question only uses "ir" I would also in the answer = Busco variedad de cosas cuando voy de compras.

As SraJMcGin says you forget (also I do) the accent in "quién". You can use regional and language option (in you have a Windows System) and add a spanish keyboard, after that select it with keyboard shortcut or change settings language in the star bar. You can see the keyboard distribution with "properties". The accent is besides the "p".